This paper introduces a new dynamic portfolio performance risk measure called Expected Regret of Drawdown (ERoD) which is an average of drawdowns exceeding a specified threshold (e.g., 10%). ERoD is similar to Conditional Drawdown-at-Risk (CDaR) which is the average of some percentage of largest drawdowns. CDaR and ERoD portfolio portfolio optimization are equivalent and result in the same portfolios. Necessary optimally conditions for ERoD portfolio optimization lead to Capital Asset Pricing Model (CAPM) equations. ERoD Beta, similar to the Standard Beta, relates expected returns of securities and market. ERoD Beta equals to [average losses of a security over time intervals when market is in drawdown exceeding the threshold] divided by [average losses of market in drawdowns exceeding the threshold]. Therefore, a negative ERoD Beta identifies a security which has positive returns when market is in drawdown. ERoD Beta accounts for only time intervals when market is in drawdown and conceptually differs from Standard Beta which does not distinguish up and down movements of the market. However, ERoD Beta also provides quite different results compared to Downside Beta which is based on Lower Semi-deviation. ERoD Beta is conceptually close to CDaR Beta which is based on a percentage of worst case market drawdowns. We have built a website reporting CDaR and ERoD Betas for stocks and SP500 index as an optimal market portfolio. The case study showed that CDaR and ERoD Betas exhibit persistence over time intervals and can be used in risk management and portfolio construction.

Speakers Bio: Stan Uryasev is Professor and Frey Family Endowed Chair of Quantitative Finance at the Stony Brook University. His research is focused on efficient computer modeling and optimization techniques and their applications in finance and DOD projects. He published three books (monograph and two edited volumes) and more than 130 research papers. He is a co-inventor of the Conditional Value-at-Risk and the Conditional Drawdown-at-Risk optimization methodologies. He is developing optimization software in risk management area: VaR, CVaR, Default Probability, Drawdown, Credit Risk minimization. Stan Uryasev is a frequent speaker at academic and professional conferences. He has delivered seminars on the topics of risk management and stochastic optimization. He is on the editorial board of a number of research journals and is Editor Emeritus and Chairman of the Editorial Board of the Journal of Risk.

Rui Ding is a PhD student in Applied Mathematics and Statistics at Stony Brook University, concentrating on quantitative finance and operations research. He graduated Magna cum Laude from Columbia University where he got his BS/MS degrees in Applied & Computational Mathematics and an MS in Financial Engineering.